Numerous formulations with the same mathematical properties can be relevant to model a biological process. Different formulations can predict different model dynamics like equilibrium vs. oscillations even if they are quantitatively close (structural sensitivity). The question we address in this paper is: does the choice of a formulation affect predictions on the number of stable states? We focus on a predator–prey model with predator competition that exhibits multiple stable states. A bifurcation analysis is realized with respect to prey carrying capacity and species body mass ratio within range of values found in food web models. Bifurcation diagrams built for two type-II functional responses are different in two ways. First, the kind of stable state (equilibrium vs. oscillations) is different for 26.0– 49.4% of the parameter values, depending on the parameter space investigated. Using generalized modelling, we highlight the role of functional response slope in this difference. Secondly, the number of stable states is higher with Ivlev’s functional response for 0.1–14.3% of the parameter values. These two changes interact to create differentmodel predictions if a parameter value or a state variable is altered. In these two examples of disturbance, Holling’s disc equation predicts a higher system resilience. Indeed, Ivlev’s functional response predicts that disturbance may trap the system into an alternative stable state that can be escaped from only by a larger alteration (hysteresis phenomena). Two questions arise from this work: (i) how much complex ecological models can be affected by this sensitivity to model formulation? and (ii) how to deal with these uncertainties in model predictions?

Scaling up the predator functional response in heterogeneous environment: When Holling type III can emerge?

Accurate parametrization of functional terms in model equations is of great importance for reproducing the dynamics of real food webs. Constructing models over large spatial and temporal scales using mathematical expressions obtained based on microcosm experiments can be erroneous. Here, using a generic spatial predator-prey model, we show that scaling up the microscale functional response of a predator can result in qualitative alterations of functional response on macroscales. In particular, a global functional response of sigmoid type (Holling type III) can emerge as a result of non-linear averaging of non-sigmoid local responses (Holling type I or II). We demonstrate that alteration between the local and the global response in the model is a result of the interplay between density-dependent dispersal of the predator across the habitat and heterogeneity of the environment. Using the method of aggregation of variables, we analytically derive the mathematical formulation of the global functional response as a function of the total amount of prey in the system, and reveal the key parameters which control the emergence of a Holling type III global response. We argue that this mechanism by which a global Holling type III emerges from a local Holling type II response has not been reported in the literature yet: in particular, Holling type III can emerge in the case of a fixed gradient of resource distribution across the habitat, which would be impossible in priorly suggested mechanisms. As a case study, we consider the interaction between phytoplankton and zooplankton grazers in the water column; and we show that the emergence of a Holling type III global response can allow for the efficient top-down regulation of primary producers and stabilization of planktonic ecosystems under eutrophic conditions.

Enhancing the predictive power of models in biology is a challenging issue. Among the major difficulties impeding model development and implementation are the sensitivity of outcomes to variations in model parameters, the problem of choosing of particular expressions for the parametrization of functional relations, and difficulties in validating models using laboratory data and/or field observations. In this paper, we revisit the phenomenon which is referred to as structural sensitivity of a model. Structural sensitivity arises as a result of the interplay between sensitivity of model outcomes to variations in parameters and sensitivity to the choice of model functions, and this can be somewhat of a bottleneck in improving the models predictive power. We provide a rigorous definition of structural sensitivity and we show how we can quantify the degree of sensitivity of a model based on the Hausdorff distance concept. We propose a simple semi-analytical test of structural sensitivity in an ODE modeling framework. Furthermore, we emphasize the importance of directly linking the variability of field/experimental data and model predictions, and we demonstrate a way of assessing the robustness of modeling predictions with respect to data sampling variability. As an insightful illustrative example, we test our sensitivity analysis methods on a chemostat predator-prey model, where we use laboratory data on the feeding of protozoa to parameterize the predator functional response.

Deterministic population models for adaptive dynamics are derived mathematically from individual-centred stochastic models in the limit of large populations. However, it is common that numerical simulations of both models fit poorly and give rather different behaviours in terms of evolution speeds and branching patterns. Stochastic simulations involve extinction phenomenon operating through demographic stochasticity, when the number of individual ‘units’ is small. Focusing on the class of integro-differential adaptive models, we include a similar notion in the deterministic formulations, a survival threshold, which allows phenotypical traits in the population to vanish when represented by few ‘individuals’. Based on numerical simulations, we show that the survival threshold changes drastically the solution; (i) the evolution speed is much slower, (ii) the branching patterns are reduced continuously and (iii) these patterns are comparable to those obtained with stochastic simulations. The rescaled models can also be analysed theoretically. One can recover the concentration phenomena on well-separated Dirac masses through the constrained Hamilton–Jacobi equation in the limit of small mutations and large observation times.